It is well known that high-frequency asset returns are fat-tailed relative to the Gaussian distribution, and that the fat tails are typically reduced but not eliminated when returns are standardized by volatilities estimated from popular ARCH and stochastic volatility models. We consider two major dollar exchange rates, and we show that returns standardized instead by the realized volatilities of Andersen, Bollerslev, Diebold and Labys (2000a) are very nearly Gaussian. We perform both univariate and multivariate analyses, and we trace the differing effects of the different standardizations to differences in information sets.